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If j > 1, is integer j a prime number? (1) When j is div

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by Anju@Gurome » Mon Apr 29, 2013 10:26 pm
varun289 wrote:If j > 1, is integer j a prime number?

(1) When j is divided by 3, the remainder is 1.
(2) When j is divided by 2, the remainder is 1.
One simple thing about prime number is they are rarely predictable and there is no formula to generate a prime number. A prime number may be represented in a particular form but that particular form will not always generate prime numbers.

So, whenever you come across this type of problem, combine both statements together and try to find contradiction. In fact, with practice you'll happen to know that answer to this particular problem is definitely E. Find a contradiction just to be more confident.

Here, if we combine both statements, it simply means when j is divided by 6 it leaves a remainder of 1. So, j is one more than a multiple of 6.

7 = 6*1 + 1 ---> 7 is prime
25 = 6*4 + 1 ---> 25 is not prime

We have our contradiction.
So, both statements together is also not sufficient.

The correct answer is E.

Go through this discussion made by Anurag on a problem testing the same concept (please scroll down and read his follow-on posts also) >> https://www.beatthegmat.com/num-prp-t74492.html#335738
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by killerdrummer » Mon Apr 29, 2013 11:10 pm
(1) When j is divided by 3, the remainder is 1.

N =3K +1

Nature of this number -> either odd or even and as we know except 2, all primes are odd .
So this option alone is not sufficient

e.g. 7,10

Insufficient.

(2) When j is divided by 2, the remainder is 1.

N= 2K+1

Nature of this number -> Odd
11 is odd and prime, but 15 is odd and not prime.

e.g. 5,9

Insufficient.

Combining 1 and 2

Nature of this number : 6K +1


Anju has explained this part already ! :)
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by Blue_Skies » Tue May 07, 2013 6:39 pm
Answer is E.
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by Brent@GMATPrepNow » Tue May 07, 2013 6:58 pm
varun289 wrote:If j > 1, is integer j a prime number?

(1) When j is divided by 3, the remainder is 1.

(2) When j is divided by 2, the remainder is 1.
When it comes to remainders, we have a nice rule that says:

If N divided by D, leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.

For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.

Okay, now onto the question.

Target question: Is integer j a prime number?

Statement 1: When j is divided by 3, the remainder is 1.
Possible values of j: 4, 7, 10, 13, 16, 19, 22, 25...
As you can see, some values of j are prime and some are not.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: When j is divided by 2, the remainder is 1.
Possible values of j: 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, ...
As you can see, some values of j are prime and some are not.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined:
From statement 1: j could equal 4, 7, 10, 13, 16, 19, 22, 25...
From statement 2: j could equal 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, ...

Some numbers that satisfy both statements are 7, 13, 19, 25, . . .
Once again, some values of j are prime and some are not.
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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